In these lessons, we will learn the concept of a set, methods for defining sets, set notations, empty set, symbols for ‘is an element of’, subset, intersection and union. These lessons are part of a series of Lessons On Sets.

**Related Pages**

Describing Sets

Venn Diagrams And Subsets

More Lessons On Sets

The following table gives a summary of the symbols use in sets.

A set is a well-defined collection of distinct objects.

The individual objects in a set are called the **members** or
**elements** of the set.

Some notations for sets are:

{1, 2, 3} = set of integers greater than 0 and less than 4 = {x: x is an integer and 0 < x < 4}

We also have the empty set denoted by {} or Ø, meaning that the set has no elements.

We can have infinite sets for example {1, 2, 3, …}, meaning that the set has an infinite number of elements.

We have a symbol showing membership. We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.

∈ denotes “is an element of’ or “is a member of” or “belongs to”

∉ denotes “is not an element of” or “is not a member of” or “does not belong to”

**Example:**

If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A

This video introduces the concept of a set and various methods for defining sets.

Set Notation(s): A discussion of set notation: lists, descriptions, and set-builder notation.

The following video describes: Set Notations, Empty Set, Symbols for “is an element of’ subset, intersection and union.

Set Notation: Roster Method, Set Builder Notation.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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